In a large pot or Dutch oven, melt the butter over medium heat.
Add the diced onion, sliced carrots, and sliced celery to the pot. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the chicken broth and bring to a boil.
Add the shredded cooked chicken, dried thyme, dried parsley, salt, and black pepper. Stir to combine.
Add the egg noodles to the boiling soup and cook according to package instructions, about 7-8 minutes, until tender.
While the noodles cook, in a small bowl, whisk together the milk, heavy cream, and flour until smooth.
Once the noodles are cooked, reduce the heat to low and slowly stir in the milk mixture.
Simmer the soup gently for 5 minutes, stirring frequently, until the soup thickens and becomes creamy.
Taste and adjust seasoning with additional salt and pepper if needed.
Remove from heat and serve hot.